群论和物理学

出版时间：2000-4  出版社：世界图书出版公司(此信息作废)  作者：S.Sternberg  页数：429  
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内容概要

Group theory is one of the great achievements of 19th century mathematics. It emerged as a unifying idea drawing on four different sources: number theory, the theory of equations, geometry, and crystallography. The early motivation from number theory stemmed from the work of Euler, Legendre and Gauss on power residues. In the theory of equations, the study of various permutation groups became increasingly important through the work of Lagrange, Ruffini, Gauss, Abel, Cauchy, and especially Galois. The discovery of new types of geometries-including non-Euclidean, affine, projective etc.-led, eventually, to the famous Erlangen program of Klein, which proposed that the true study of any geometry lies in an analysis of its group of motions. In crystallography, the possible symmetries of the internal structure of a crystal were enumerated long before there was any possibility of its physical determination (by X-ray analysis).

书籍目录

Preface1 Basic definitions and examples　1.1 Groups: definition and examples　1.2 Homomorphisms: the relation between SL 2, and the Lorentz group　1.3 The action of a group on a set　1.4 Conjugation and conjugacy classes　1.5 Applications to crystallography　1.6 The topology of SU 2 and SO 3　1.7 Morphisms　1.8 The classification of the finite subgroups of SO 3　1.9 The classification of the finite subgroups of O 3　1.10 The icosahedral group and the fullerenes2 Representation theory of finite groups　2.1 Definitions, examples, irreducibility　2.2 Complete reducibility　2.3 Schur''s lemma　2.4 Characters and their orthogonality relations　2.5 Action on function spaces　2.6 The regular representation　2.7 Character tables　2.8 The representations of the symmetric group3 Molecular vibrations and homogeneous vector bundles　3.1 Small oscillations and group theory　3.2 Molecular displacements and vector bundles　3.3 Induced representations　3.4 Principal bundles　3.5 Tensor products　3.6 Representative operators and quantum mechanical selection rules　3.7 The semiclassical theory of radiation　3.8 Semidirect products and their representations　3.9 Wigner''s classification of the irreducible representations of the Poincare group　3.10 Parity　3.11 The Mackey theorems on induced representations, with applications to the symmetric group　3.12 Exchange forces and induced representations4 Compact groups and Lie groups　4.1 Haar measure　4.2 The Peter-Weyl theorem　4.3 The irreducible representations of SU 2　4.4 The irreducible representations of SO 3 and spherical harmonics　4.5 The hydrogen atom　4.6 The periodic table　4.7 The shell model of the nucleus　4.8 The Clebsch-Gordan coefficients and isospin　4.9 Relativistic wave equations　4.10 Lie algebras　4.11 Representations of su 25 The irreducible representations of SU n　5.1 The representation of Gl V on the r-fold tensor product　5.2 Gl V spans Hornsr TrV, TrV　5.3 Decomposition of TrV into irreducibles　5.4 Computational rules　5.5 Description of tensors belonging to W　5.6 Representations of Gl V and Sl V on U　5.7 Weight vectors　5.8 Determination of the irreducible finite-dimensional repre-sentations of Sl d, C　5.9 Strangeness　5.10 The eight-fold way　5.11 Quarks　5.12 Color and beyond　5.13 Where do we standAppendix A The Bravais lattices and the arithmetical crystal classes　A.1 The lattice basis and the primitive cell　A.2 The 14 Bravais lattices　　Appendix B Tensor product　　Appendix C Integral geometry and the representations of the symmetric group　C.1 Partition pairs　C.2 Proof of the main combinatorial lemma　C.3 The Littlewood-Richardson rule and Young''s rule　C.4 The ring of virtual representations of all the Sn　C.5 Dimension formulas　C.6 The Murnaghan-Nakayama rule　C.7 Characters of Gl V　　AppendixD Wigner''s theorem on quantum mechanical symmetries　　Appendix E Compact groups, Haar measure, and the Peter-Weyl theorem　　Appendix F A history of 19th century spectroscopy　　Appendix G Characters and fixed point formulas for Lie groupsFurther readingIndex

用户评论 (总计19条)

•   英文版，不错
•   此书算是群论中较为高级的读本，内容精炼，发人深思，建议读此书前要有一定的群论基础。
•   内容较深，推荐对群论有一定基础的同学阅读。
•   服务不错不错，商品也可以，我是当当的老客户了
•   还没有读，浏览了一下。感觉很好！
•   我比较喜欢的书，简单精炼
•   作为群论基础学习，专业选修，应该不错吧
•   帮别人买的，不知如何
•   质量不错 价格小贵了点
  
  评论过程怎么这么繁琐啊 简单一点行吗
•   适合理论物理的研究生读
•   感觉和晶格相关多了点
•   纸张质量较差
•   印刷质量差了，其他还好
•   写的一般；符号不好，讲解条理不简洁清晰！
•   比樱井的《高等量子力学》要薄，价格却是后者的一倍。但话又说回来，内容相当好，我看重的就是这点。
•   物理前沿的必修课～
•   快递超慢，到货时书已经面目全非了，封面有何种划痕和凹痕，不知是快递粗暴还是书库粗暴
•   只讲到了第一章，写的不错，其他内容没仔细看呢。就是太贵了有木有？
•   纸张很薄，没看过书店卖的是怎样的，不过拿到手的这本书的纸质太令我失望了。